Frequency discriminator employing multiply resonant piezoelectric vibrator



Jan. 29, 1957 G. w. WILLARD FREQUENCY DISCRIMINATOR EMPLOYING MULTIPLYRESONANT PIEZOELECTRIC VIBRATOR 6 Sheets-Sheet 1 Filed Oct. 28. 1950ATTORNEY D on ,ma Mn. n N fu /I d Jan. 29, 1957 G. w. WILLARD 2,779,191

FREQUENCY DISCRIMINATOR EMPLOYING MULTIPLY RESONANT PIEZOELECTRICVIBRATOR Filed Oct. 28, 1950 6 Sheets-Sheet 2 FUNDAMENTAL rH/RoHARMo/v/c /NVENTOR G. W. W/LLARD www A TTORNEV n l. .l H

G. w. WILLARD 2,779,191 FREQUENCY DISCRIMINATOR EMPLOYING MULTIPLYRESONANT PIEZOELECTRIC VIBRATOR Filed Oct. 28, 1950 6 Sheets-Sheet 3Jan. 29, 1957 F/G.6 F/G. 7

HH HHH! H||| HH/ G. W. WILL/4R0 BLW M A TTORNEV Jan, 29, 1957 G. W.WILLARD 2,779,191

FREQUENCY DISCRIMINATOR EMFLOYING :Manny RESONANT PIEZOELECTRC VIBRATORFiled Oct. 28, 1950 6 Sheets-Sheet ,4

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/Nl/EA/ TOR G. W. W/L/ ARD @QM w ATTORNEY Jan. 29, 1957 G. w. WILLARD2,779,191

FREQUENCY DISCRIMINATOR EMPLoYxNG MULTIFLY REsoNANT PIEZOELECTRICVIBRATOR Filed OCT.. 28, 1950 6 Sheets-Sheet 5 @Hm [El] la @j la asn/oal (Elim MH la /NVENTOR G. W. W/L ARD BQMWM ATTORNEY Jan. 29, 1957 G. w.WILLARD 2,779,191

FREQUENCY DISCRMINATOR EMPLOYING MULTIPLY RESONANT PIEZOELECTRICVIBRATOR Filed Oct. 28. 1950 6 Sheets-Sheet 6 OU TPU T F/G. 26 r-H/NVEA/TOR G. W. W/LLARD A TTOR/VE V United States Patent FREQUENCYDISCRDIINATOR EMPLOYING MULTIPLY RESONANT PIEZOELECTRIC VIBRATOR GeraldW. Willard, Fanwood, N. J., assigner to Bell Telephone Laboratories,Incorporated, New York, N. Y., a corporation of New York ApplicationOctober 28, 1950, Serial No. 192,765

9 Claims. (Cl. 73--67.8)

In my copending application Serial No. 17,272, filed March 26, 1948, nowUnited States Patent No. 2,549,872, issued April 24, 1951, assigned tothe same assignee as the present application, I have described curvedpiezoelectric radiators of uniform thickness which vary in resonantfrequency from point to point over their surface due to the fact thatthe curved radiator has a frequency constant which varies over thesurface, and this in turn is due to the variation in the orientation ofthe radiating surface with respect to the crystallographic axes of theradiator.

A somewhat similar variation in resonant frequency is obtainable in awedge of piezoelectric material by virtue of the varying thickness,although the orientation of the radiating surface and hence thefrequency constant of the radiator may be the same in all portion of theradiator.

In accordance with the invention, a radiator of variable resonantfrequency is located in contact with a suitable vibration transmittingmedium and is provided with operating electrodes arranged to impress anelectric potential variation over substantially the whole radiativeSurface of the radiator. Any region of the radiative surface which isresonant to the impressed potential variations or to any frequencycomponent of a complex impressed potential variation is excited therebyinto localized vibrations which may result in a beam or beams ofvibrational waves being radiated into the contiguous medium. Theradiated beams of vibrational waves impinge upon `a plurality of elastictransmission members disposed in contact with the transmitting mediumand ex# cite those members which are resonant to the radiatedvibrational waves. Resonant condition responsive devices coupled to theresonant members indicate such factors as the particular frequencies inthe complex irnpressed potential variation, the velocity of the radiatedbeams through certain transmission media, or the dimensional propertiesof a particular resonant elastic transmission member.

In the drawings:

Fig. l is an isometric view of the mechanical and optical parts of anarrangement for measuring the frequency of an oscillating electricsignal;

Fig. 2 is a side view of the arrangement of Fig. 1, omitting opticalparts but indicating a radiated sound beam;

Fig. 3 is a top view of the arrangement of Fig. l, omitting opticalparts;

Figs. 4, 5, 6, and 7 are screen patterns such as may be obtained withthe arrangement of Fig. 1 under different conditions;

Figs. 8 and 9 are diagrams useful in explaining the operation of a wedgeradiator at fundamental frequency;

Figs. 10 and l1 are diagrams useful in explaining the operation of awedge radiator at third harmonic frequency;

Figs. l2, 13, and 14 are diagrams used in explaining a ICC theinterrelation of the thickness, frequency, 'and beam width functions ofa radiator;

Figs. 15, 16, 17, 18, and 19 show means of overcoming extraneous modesof vibration in a wedge radiator;

Figs. 2O and 21 show three-channel voice systems in which an arrangementaccording to the invention is used as a channel filter;

Fig. 22 is a schematic diagram of an ultrasonic delay line employing thewedge radiators;

Figs. 23 and 24 are schematic diagrams showing applications of theinvention to measurements of thickness or other properties of sheetmaterials;

Figs. 25 and 26 are top and side view schematic diagrams, respectively,of an application of the invention to a velocity measuring system;

Fig. 27 is a schematic diagram of a broad frequency band light modulatorembodying the invention; and

Fig. 28 is an orientation diagram for a specifically orientedcylindrical quartz vibrator for use as a channel filter.

Fig. 1 shows the arrangement of the acoustic and optical parts of anequipment for measuring the frequency of an oscillating electricalsignal. The electric signal whose frequency it is desired to know issupplied by a generator 1 which is connected to the electrodes 2 and 4of a piezoelectric transducer 3. The transducer 3 has the form of a thinwedge with rectangular edge boundary and may be made of X-cut quartz,for example, in which case the X-crystallographic axis thereof should bein the direction of the thickness of the wedge, that is, approximatelynormal to the electrode faces 2 and 4. As here shown, the taper of thewedge 3 is from thick at the top to thin at the bottom, the exact natureof the taper being described later. As described under succeedingfigures, the transducer assembly 2, 3, 4 closes the end of a tank 5 sothat the latter may contain an acoustic transmitting liquid 6. The tankhas two parallel major faces 7 and 8 made of optical glass plates sothat light may be passed undeviated through them. In the far end of thetank, an acoustic absorbing pad 9 is placed to absorb without refiectionall sound waves incident thereon and hence to prevent any standing wavepatterns being formed. The liquid medium 6 may be any of a number ofacoustically and optically transmitting mediums, for example, water. Thepad 9 may be one of the synthetic rubbers which is sufiicientlyattenuating and whose acoustic impedance (density times velocity)matches that of the liquid medium 6. The tank 5 and its contents willhereinafter be called the sonic unit.

The optical system comprises a number of elements arranged along theoptical axis 10, said axis being fixed perpendicularly to the windows 7,8 and parallel to the radiator electrode surfaces of elements 2, 3 ofthe sonic unit 5. A source 11 sends light through a condenser lens 12and through a pinhole 14 in an aperture plate 13. ln many cases, thepinhole 14 may be replaced by a long narrow rectangle with its length inthe vertical direction, parallel to the radiator 2, 3, 4, and its widthequal to the diameter of the pinhole as hereinafter described. This,together with a similarly elongated light source, gives increasedillumination. A lens 15 collimates the light from the pinhole 14 throughthe sonic unit where a focusing lens 16 refocuses the light onto anopaque pinhead aperture 17 mounted on a slender support 18.Alternatively, 17 may be an opaque disk on a transparent plate. Thediameter of the pinhead 17 is equal to or slightly larger than the imageof the pinhole falling upon it, thus stopping all light passage when nosound waves are present in the sonic unit. If the pinhole 14 is replacedby a rectangular hole, the pinhead 17 is to be replaced by an opaquerectangle. Further, the pinhead aperture 17 may be replaced by a pinholeaperture of the same shape as the pinhole aperture 14. These details andtheir effect are well known. The diameter d of the pinhole 14 is wellknown to be determined from the focal length F of the lens 15, theshortest wavelength of light used AL, and the longest wavelength ofsound to be used AS by as shown, for example, in the following publishedreferences:

(1) G. W. Willard, United States Patents Nos. 2,345,441 and 2,287,587.

(2) G. W. Willard, I. A. S. A., 21 (10i-108), March 1949.

(3) L. Bergman-H. S. Hatfield, Ultrasonics (John Wiley and Sons,Incorporated, New York, 1939).

When sound waves are passing through the sonic unit 5, some of the lightnormally striking the pinhead 17 will be diffracted and pass by thepinhead through a projecting lens 19 and onto a screen 20 so that apoint such as 21 in the center plane of the sonic unit 5 is imaged atthe point 21' on the screen 20. Similarly, the electrode face 2 of theradiator 3 is imaged as 2', and transparent scales 25 and 27, to bedescribed, yare imaged as 25' and 27'. Thus, the whole view on thescreen 20 is a reversed image of the central object plane of the sonicunit 5, the boundary 31 corresponding to the illuminated area in 5, twoof whose limiting light rays are 29 and 30. When a sound beam 24 (notshown in this view) is radiated from an area 23, for example, of theradiators 2, 3, 4, it will traverse the tank to the pad 9 and will beimaged on the screen as a bright band 24', the height 2Ay' of 24' beingequal to the height 2/ \y of 23 multiplied by the optical magnefication,which is given by the ratio of the distances 19 to 21 and 19 to 21.Transparent scales 25 and 27, slidingly mounted on supports 26 and 28,are used to measure the length or the height, respectively, of theradiated sound beam.

Fig. 2 shows a side View and Fig. 3 shows a top view, sectional at 3-3of Fig. 2, of the sonic unit 5 of Fig. l. The scales 25 and 27, mountedon supports 26 and 28, respectively, are shown in this figure positionednear to the sound beam 24 radiated from the area 23 of wedge radiator 2,3, 4. The circle 31 encloses the illuminated area of the sonic unit andis imaged on the screen 20 of Fig. 1, and Figs. 4, 5, 6, 7, as 31. Theoptical object plane in the tank is normal to the optical axis, 10,parallel to the windows 7 and 8, and lies mid-way between 7 and 8. Thequartz wedge 3 is metallized, as by evaporation, on the inner major faceand the edges to form the electrode 2 and to provide means of solderingaround the edges to reentrant rectangular sleeve 5'. Thus, electrode 2is electrically continuous with the metal parts of the tank 5 and may beelectrically connected to the signal source 1 at any point of the tank,as at 2. The outer electrode 4 may be also metallized and connected asby soldering at 4', or 4 may be a flat stiff metal plate lightly sprungagainst 3. In any case, electrode 4 is appreciably smaller than the faceof the wedge 3 to provide electrical insulation from 2. Preferably, 4 issuiciently smaller than the face of 3 that the electric field betweenthe two faces of 3 is unaffected by edge metallization of the wedge.Thus, no mechanical vibration will occur in the wedge around itsperiphery where it is attached to the sleeve 5'. The windows 7, 8 ofoptical plate glass may be cemented into the tank 5 o`r may bemetallized on the edges and soldered in place. In the latter case, thesonic unit 5 is suitable to contain any non-corrosive liquid that it maybe desired to use and, if electroplated after assembly with the propermetal, could be used for many corrosive liquids.

Figs. 4, 5, 6, and 7 are screen patterns like that shown on the screen20 of Fig. l, each for a different condition of operation. It is to berecalled that these images are optically reversed from the array in theobject plane of the sonic unit, as will be seen by comparing the primeddesignations of the image with their un-primed designations in theobject plane of the sonic unit of Figs. l, 2, 3.

It will be convenient in describing Figs. 4, 5, 6, and 7 to refer to theimages as though they were the actual objects in the sonic unit 5. Thus,3' may be called the radiator, and its thickness as later used will bet, and the height of the sound beam 24 will be hereinafter called Zay,as shown in Fig. 4.

When using the assumed pinhole 14 and pinhead 17 apertures and when nosignal is applied to the radiator 2, 3, 4, the image will be mainlyrelatively dark, being illuminated only by scattered light passing thepinhead 17. The region from 2' to 31' will be entirely black, since theradiator 2, 3, 4 and its mounting entirely cut off the light The scaleimages 25' and 27' may be quite bright if the scales 25 and 27 areproperly made, say by opaquely coating a transparent plastic and thenengraving the markings through the opaque coating. When a sound beam `ispresent inthe sonic unit, it will be imaged by the bright band 24 in anotherwise dark eld, although in the figures, 24' is shown forconvenience as dark in a bright field.

A negative of this image would be obtained if the aperture pinhead 17were replaced by a pinhole, as at 13, 14, as previously explained. Thislatter arrangement is usually not preferred, since the picturedefinition is reduced due to the smallness of the bundle of rays whichthen pass through the plane of 17 to form the image.

Fig. 4 shows the screen pattern when the wedge radiator 3' is operatedin its fundamental mode, the applied signal having a frequency f forwhich the radiator thickness t, at the location corresponding to thecenter of the beam 24', is resonant. For example, assuming that thefrequency constant of the radiator is K=2860 kc.mm., then f inkilocycles is given by where t is in millimeters. Thus, at theparticular location along the wedge labled as t in the figure, theradiator will be excited at resonance, and a maximum of sonic energywill be radiated into the liquid. At other locations along the radiator,receding from this location the wedge, though excited electrically overits whole vertical height, the radiator will be excited increasingly offresonance and hence will radiate decreasing intensities of sonic energyinto the liquid. Thus, the beam 24 will be most intense at its center,and the intensity will decrease on each side of center on recedingtherefrom. Though the beam 24' is indicated to have sharp boundariesseparated by the distance 2Ay, actually there are no sharp boundariesobserved, the intensity grading off gradually. However, as explainedlater, the width ZAy is definitely related to the intensity distributionby being the width of the beam between the points where its intensityhas dropped to one-half value. This definition of the beam width is asuseful in later comparisons as though the beam had definite boundaries.

It is evident from Fig. 4 that the width of sound beam is decreased ifthe degree of taper of the wedge radiator is increased. For the radiator3 shown here with plane faces 2 and 4', the degree of taper may bedoubled by doubling the angle between the faces 2 and 4', and this Willresult in decreasing the beam width 2Ay to one half its previous value.At the same time the range of frequencies, from a minimum value fi atthe thick end to a maximum of f2 at the thin end, will increase todouble with the doubling of the taper angle.

If either the degree of taper or the length of taper or both areincreased to or beyond the amount where the thick end is equal to orgreater than three times the thickness of the thin end, then fzSfi, andan ambiguity may result from the fact that the radiator may radiate intwo places at once. This is true, since for any given thickness ofradiator ta, the radiator may vibrate in any odd harmonic of thefundamental frequency fg. such that f -a-nfa, where n is odd. Use ofthis harmonic operation will be referred to in the following sections ofthis specilication. -In the present case, it is, however, assumed thatthe frequency range is limited by restriction to f2 less than 3f1. Thus,for a signal whose frequency is varied between fz and fr, the radiatedsound beam will slide up and down in the field, always being radiatedfrom the location where the thickness t is correct to obtain resonanceat the instantaneous value of the frequency. Hence, a properlycalibrated scale 27 may be used to determine the frequency of signalthat is applied to the radiator, the center of the sound beam 24' beingused as the index point. If -the applied signal has components of threefrequencies fr, fj, fk within the range fr to f2, then three individualbeams will be radiated; and, providing their separations are not tooclose, each frequency may be determined.

Let it be summarized that for fundamental operation, as in Fig. 4, therange of frequencies that may be determined is from fr to 3ft. Thisoperation is most useful where the required range of frequency is large.As the range is restricted, the width of sound beam ZAy is increaseduntil the point where it appears to cover the whole field of view, itscenter cannot be determined, and thence the applied frequency isundetermined.

Fig. 5 shows the screen pattern when the radiator is operated in thethird harmonic mode so that The sound beam Zay is now reduced to onethird the value that would prevail were the same radiator operated in'the fundamental mode, as will be explained hereinafter. However, toprevent the ambiguity resulting from radiation of two sound beams for asingle signal frequency, the range must now be restricted to between frand (5/3)fi, which may be accomplished by keeping the thick end of theradiator less than 5/3 as thick as the thin end. -It is seen then thatthe third harmonic operation of the radiator provides greatersensitivity in measuring frequency, since 2Ay is reduced, but over anarrower range of frequencies than was possible with fundamentaloperation. It might be parenthetically noted that this same radiatordesigned to be operated over the range of frequencies fr to (5/3)f1 inthird harmonic may also be operated in the fundamental mode merely byapplying frequencies within the range (l/3)f1 to (5/9)f1. However, asnoted before, the width of sound beam 24' will then be three times asgreat as when properly used in the third harmonic mode, and sensitivitywill be reduced.

Fig. 6 shows the screen pattern when the radiator is operated in the fthharmonic mode so that Here, the sound beam width is reduced to one fifththat prevailing when the same radiator is operated in the fundamentalmode. The unambiguous frequency range is now reduced to the range fromf1 to (7/5)f1, which restriction is accomplished by making t1 less than(5/ 7) t2. Thus, as the order of harmonic is increased, thc range isdecreased but the sensitivity is increased.

Fig. 7 shows the screen pattern when the radiator is operated in anymode, use being made of both scales and 27', the latter being used aspreviously described in Fig. 4 to indicate the frequency of the appliedsignal, the location of the sound beam 24 along the suitably calibratedscale 27' determining the frequency. The scale 25', on the other hand,may be used to indicate the relative intensity of the applied electricsignal. In this case, the liquid transmitting medium is chosen to have asuitable attenuation so that the strongest signal received will producean apparent length of beam 24 which just crosses the field of view.Then, weaker signals will have shorter (horizontal in Fig. 7) lengthswhose end position 24" is measured on the scale 25. Thus, with asuitably calibrated scale, the strength of the signal, as well as thefrequency, may be determined. The choice of a suitable liquid may beeasily made by consulting the literature, e. g., G. W. Willard,Ultrasonic Absorption and Velocity Measurements in Numerous Liquids, J.A. S. A., vol. l2, No. 3, 438-448, January 1921. Liquids of intermediateattenuations may be obtained by mixing, as in United States Patent No.2,407,294, William Shockley and G. W. Willard.

Figs. 8 and 9 are used to exxplain the operation of a wedge radiatoroperated in its fundamental mode of thickness vibration. Fig. 9 shows aportion of a wedge whose thickness t varies with distance y along thewedge. When the radiator is made of piezoelectric quartz, thet-direction may be parallel to the crystallographic X-axis of thequartz, while the y-direction may be some crystallographic directionnormal to the X-axis. Electrodes are assumed adjacent to the majorsurfaces of the wedge material, i. e., the surfaces approximatelyperpendicular to the t-axis. In Fig. 8 is shown, along the f-axis, apossible distribution of resonant frequencies along the wedge,calculated from the formula The curve shows the relative radiated soundamplitudes in the adjoining sound transmitting medium when the radiatoris driven at the frequency l0 megacycles. For the point 32, thethickness of the radiator is exactly correct for the radiator to be inresonance at lO megacycles. The amplitude of the sound beam at thispoint is taken as Ar, subscript r indicating the resonant condition. Forany other location, the amplitude will be less, for at other locationsthe radiator is being excited olf resonance. Thus A/Af is the ratio ofthe amplitude A at any location relative to Ar at the resonant location.It is well known that A/Ar varies with frequency, for a normal planeparallel radiator, according to .Mami/9% (6) where Q is a function ofthe ratio of the driving frequency to the resonant frequency, as shownin my above-identified Patent No. 2,549,872, and in my article inJournal of Acoustical Society of America, 2l, pages 360-375, July 1949.The two points 33 on the curve indicate that at the locations where thenatural resonant frequency is 9.5 and 10.5 megacycles, respectively, thesound amplitude is reduced to one half that occurring at thelO-megacycle location, a condition about correct for X-cut quartzradiating into water on one side only. The frequency separation betweenthese two points is 2Af and corresponds to a location separation of 2f\y. The amplitude of the sound beam falls oli rapidly outside the regionbetween the points 33, soon becoming ineffective for any purpose. Whilethe width of the sound beam in the yaxis direction has no denite value,its effective width is limited. Since the effective width varies-withthe degree of taper of the wedge, the thickness of the wedge and thematerial of the wedge and of the medium into which it radiates, and themode of operation, it is useful to define an arbitrary numerical widthfor the beam which then may be related to the quantities affecting thespread. For this purpose, the width of the beam is defined to be thedistance Zay between the points 33, where the amplitude ratio A/Ar justfalls to one-half value. At each of these points, the driving frequencyis designated as nf different from the resonant frequencies for thesepoints.

Figs. l0 and 1l explain the operation of a wedge radiator operated inits third harmonic mode. The frequency range used here is chosen to bethe same as that used in Figs. 8 and 9, so that here the radiator mustbe three times as thick as in Figs. 8 and 9. The explanation of Figs. 8and 9 applies also to Figs. 10 and 11, except that in the latter casethe points 33 for half amplitude A/Ar=/z occur for Af, and Ay havingvalues one third that previously found, as will be shown hereinafter.Thus, a third-harmonic radiator will radiate a sound beam only one thirdas wide as a fundamental radiator of the same frequency range. Theoptical effects resulting from such wedges mounted as in Figs. l, 2, 3,is shown in Fig. 4 for fundamental operation (as explained in Figs. 8and 9), Fig. 5 for third harmonic operation (as explained in Figs. l andl1), and Fig. 6 for fth harmonic operation. Thus, where frequencydiscrimination is desired, it is preferable to use harmonic operation ofthe radiator. It is well known that any thickness mode radiator may beoperated at any of its odd harmonics as well as its fundamental mode, Ndenoting the order and being l. 3. 5, in the frequency determiningequation where K is a constant of the material and t the thickness.

Figs. 12, 13, and 14 are used to explain the mathematical relationbetween thickness t, frequency f, and beam width 2Ay for a wedgeradiator.

In Fig. 12, the wedge shape cross section of the radiator is shown inthe (y, t) coordinate plane, the length of the radiator in they-direction being l, and the length in the z-direction normal to thefigure being designated as z. Strictly speaking, the major dimensions land z are of the electrode area of the radiator only since in general,as previously pointed out, the electrodes do not go to the edges of theradiator. In the present case, Fig. l2, the thickness t varies withlocation g according to where t=ta at y=0, the thick end; andt=tb=ta(lal) at the thin end, a being a constant. If it is desired touse this wedge in fundamental operation, tb should not be less than onethird as large as ta to avoid double radiation and ambiguity, aspreviously described. Suppose, as shown in the ligure, th=ta/3, then itcan be derived that Fig. 13 shows the resonant frequency of the wedge asa function of location y along the wedge. If fa=K/ta, where K is thefrequency constant of the material, then ,fa is the fundamental resonantfrequency of the wedge at the thick end y=zero, and at any otherlocation, the fundamental resonant frequency is and varies increasinglyfrom fa to Sfa. In third harmonic operation, not shown,

whence Solving (l2) for the band width.

2( l-ay) Al f1 f.,

Now, from the definition of Af, the ratio Af/fy must have the specificvalue that will make A/Af=l/2, as previously described. It is known that2Ay= (lil) where Af/fr may be taken as Af/fy in our present case,

as may be seen by reference to my article in Journal of AcousticalSociety of America, July 1949, cited. It is evident that at the edge ofthe band A/Af=1/2=1/(i+4M2c2)1/2 (17) from which it follows that 3Cz-LMZ (18) For an X-cut quartz wedge radiating into water, M isapproximately ten, whence That is, the sound beam width is a function oflocation along the radiator (or of frequency at which it is excited) andvaries from 0.l5l at y=0 to 0.051 at y=l. l

If in Fig. l2, the wedge had been chosen three times as thick, so thatry'==ta'(l-ay)=3la(lay) (22) varying from 3ra. to ta, and if operated inthe third harmonic, it would have the frequency relation which is onethird the value found for Fig. 14.

For some applications, it is desirable to shape the taper in such amanner that the frequency scale will be linear or that it will vary insome specified manner with y. Or it may be desired that the sound beamwidth 2Ay be independent of y or have some desired relation to y. Theserequirements may be met by suitable choice of the taper function. Forthis purpose, let us define (y) as a function of y which variescontinuously and increasingly from (0)=l at y=0 to (l)=k at y=l. Then,

will give the nth order harmonic frequency as a function of y, whichwill vary from N fe at y=0 to k-Nfe at y=l, N having odd positive valuesand f, being the fundamental resonant frequency at y=0. Then, sincefa=K/ta, ty=la/(y), it can also be shown that (2Ay)=(2b/N)((y)/'(y))(28) where b=Af/fr has the proper value as obtained from for theparticular radiator and sound medium materials Used, and (y)=(d/dy)(y)Further, it may be desired to have the radiated sound power vary in somespecified manner with location y. The radiated sound power is given byW= V2A/Rf, where V is the applied voltage, Rr is the radiationresistance per unit area, and A=(2Ay)z is the area of the radiationregion. It is known from the July 1949 article that Rr=(const)/fr2, frbeing the fundamental resonant frequency Nfy/N. Hence,WotV2(2Ay)'(Ny/N)2, or

W=kV23(y)/N3'(Ay) (30) ln other cases, it may be desired that theoptical effect Le for light passing in the y-direction of the wedgeremain constant. Now Le will be constant if the product of soundamplitude (W/A)% and beam width (Zay), i. e., (W/A)1/2'2/.\y=Le=const.Now,

Table I lists a number of examples of frequency functions (y), and listsfor each the corresponding fy, zy, Zay, W, and Lc functions. Case I is aperfectly general case, and Case II is a general power function case.Cases IIA, 11B, IIC, and IID are special cases of Case II.

Case IIA has special merit for measuring frequencies, in that thefrequency scale f is linear with location y.

Case IIC has special merit for delay lines, since the radiated soundpower is independent of frequency f and location y.

Case llD has special merit for broad-band light valving where it isdesired that light transmisison function Le be independent of location yand frequency f. In this case, the y-axis of the radiator is madeparallel to the optic axis of the optical system.

Case III has special merit for applications where it is desired that theradiated sound beam have a width which is independent of location andfrequency.

For other applications, it may be desired that driving voltage requiredto obtain a given power output W be proportional to l/ f2. Thiscondition is obtained in Case IIB. f

It is thus seen from the examples cited that the general equations ofCase I may be used to work back from some specific requirement on 2Ay,W, Le, or V to determine the necessary (y) function and hence therequired taper, t=ta(y).

Table l examples of functions (here f=Nfy as used in the text)W=(k-V2/N3a) l-ay)1, which is proportional to f Lc=(KV/N2a), which isindependent of y and f lII=exponential function; =ey; q5=aey; n 0z=Nfaeay t=tae-all 2 \y=(2b/Na), which is independent of y and f W=(V2/N3a)e21y, which is proportional to f2 Lc=(KV/N2a)eay, which isproportional to f Figs. l5, 16, l7, 13, and 19 are used to explain anoccasionally observed extraneous, undesired effect in wedge radiatorsand to show several means for alleviating this condition.

Fig. l5 shows how an internal wave in the wedge, which at the right sideof the radiator is essentially normal to the radiator surfaces where itis generated, may upon multiple reflections in the wedge be propagatedto the left-hand thick edge of the radiator. ln some cases where thethick end of the wedge is terminated in an edge face which isessentially normal to the major wedge faces, the internal wave may bereflected back along paths which are parallel to the original path, andstanding waves may be set up. When this condition occurs, there can benumerous narrow radiation regions shown by the arrows external to theradiator.

Fig. 16 shows a means of eliminating this extraneous standing waveeffect by inclining the end face of the radiator at an anglesubstantially different from normal to the major faces.

Figs. 17 and 18 show other means of eliminating the effect by making thethick end face curved: concave in Fig. 17 and convex in Fig. 18.

Fig. 19 shows another means of treating the end face for the samepurpose by attaching thereto an absorbing impedance matching mass toprevent reflection at the thick end.

Fig. 20 shows a channel filter system in which a wedge radiator 40 isused on the input end, the wedge having a frequency range equal to threetimes the frequency seperation of the channels. Three separate signalsources 41, 42, 43 may be connected to a single pair of conductors 44,travel over the same to a point where it is desired to reseparate thesignals, and then be separated out to three separate terminations 45,46, 47, each one receiving its own proper signal. At the end of thesonic unit opposite the wedge radiator are three piezoelectric pick-ups48, 49, 50, each connected to one of the respective terminations 45, 46,47. The sonic unit is designated by 5l, and no optical unit is needed.The respective 11 sound beams are indicated at 52, 53, and 54. Thepiezoelectric units 48, 49, 50 are preferably tapered and may be cutfrom a wedge radiator like radiator 40. The units 48, 49, 50 may also bereplaced by a single receiver wedge with a single electrode exposed tothe liquid and three insulated back electrodes, one connected to each ofthe terminations 45, 46, 47 in the proper order of thickness regions inthe receiver wedge.

Fig. 2l shows another channel filter system operated like that describedin Fig. 20, except that here the radiator is not in the form of a wedge,a different property of the radiator being used to obtain the sameeffect. As has been shown in my above-noted Patent No. 2,549,872, acurved radiator composed of piezoelectric crystal quartz may have aradiation region which varies in location in a manner similar to thathere above described for a wedge. Fig. 34 of my above-noted Patent No.2,549,872 is described as showing what thickness corrections would berequired to obtain a constant resonant frequency over the wholeradiator. However, if the radiator is made of uniform thickness, thefigure shows equally well how the resonant frequency would vary fromthat at the center. Thus, if one makes a cylindrical shell radiatorwhose curvature is in the plane 9=+35, according to the description inmy above-noted Patent No. 2,549,872, and whose effective curveddimension runs from a= (i. e., X-cut), at one end to a=30 (i. e., 30 offX-cut), at the other, the resonant frequency will vary from fo at theformer end to 1.16 fo at the latter end. Thus, as the frequency of thevoltage applied to the radiator varies from fo to 1.16 fo, infundamental operation, or from Nfo to 1.16 fu in nth order harmonicoperation, the radiation region moves along to the location where theradiator is in resonance with the applied frequency, thus acting justlike previously-described wedge radiators. A radiator like Fig. 40 of myabove-noted Patent No. 2,549,872, except that line D-D makes an angle of+35 degrees with Z-Z and the generatrix makes an angle of -55 degreeswith Z--Z, may be used in the arrangement of Fig. 2l herein, only onehalf of the curved portion being needed, the half to either side of theline X-G-C-G-G, as shown at 208 in Fig. 28. The curved cross section ofsuch a radiator 55 is shown connected to the signal sources 41, 42, 43.The pick-up may be plane or preferably curved to match. A curved tank 56is shown with three receiving crystals 57, S8, 59 mounted opposite theexcited regions of the radiator 55. The sound beams are indicated at 60,61, 62.

Fig. 22 shows an ultrasonic delay line in which two wedge radiators areused, R1 at the input end and an identical radiator at the output end,the internal major faces being parallel to each other. This use of wedgeradiators instead of the more conventional constant-thickness radiators,as shown, for example, in United States Patent 2,407,294, September 10,1946, permits the use of a wide frequency band without the necessity ofusing liquid mercury o1' a solid sound wave propagating medium, so thatwater may be used.

Fig. 23 shows application of a wedge radiator 63 to the measurement ofthe thickness t of specimen 64 of a sheet material. As shown in thefigure, it is assumed that the material is a metal and, therefore,electrically conducting. The wedge radiator with a single exteriorelectrode may be held against the sheet with a thin interlaycr of water,oil, etc. The signal generator, shown at 65, may be equipped to supply avariable known frequency, controlled as by a variable condenser 66, andto have means for indicating the voltage and current supplied to theradiator, or voltage and current in the plate circuit of the last tube,a meter 67 being provided for such purpose. As is common practice, thefrequency is varied u util resonanceuinthtespeimen is observed (as by asharp rise of current to a maximurnord'rop'f voltage, or both). Two suchconditions are shown schematically in the ligure, one at f7 for whichthere are n=7 one-half wavelengths of standing waves in the testspecimen, and fs the next higher frequency for which n=8. However,before calculation, the values of n are not known, only the values of fnand next higher adjacent frequency fum. It is also assumed that fromprevious test, the sound velocity in the material is known to be v. Now,the wavelength in the material is given by l=1/znl\n and by f=v/.\n.Hence fn/n=fn+i/(n+l), n=fn/ {fuer-fn), t=l/z-n \n=nv/2fn or finally=1V/2(fn+1-n) (32) The advantage of using a wedge radiator is in givinga larger frequency range over which resonances may be obtained. For, ifthe plate is so thin that only a few half wavelengths may be obtained,only a wedge radiator will radiate effectively over a suiciently widefrequency range. Further, even for thicker test plates where n is large,the accuracy of locating the exact resonant frequency may be sufcientlysmall that n=fn/(fn+i-fn) is not determined to -tell whether n equalssay l5 or 16. In this case, t is determinable only within an accuracy ofone-fifteenth or seven percent, whereas with the wedge radiator, itwould be possible to go from fn to fum, where m=2, 3, 4, in whichccaset=mV/2(fn+mfn) (33) where m is the number of regions between resonances.

Fig. 24 shows another arrangement forl measuring thickness of materialwhere a wedge radiatof'radiates into a liqiddium 69 in a tank 70 withwindows parallel to the plane of the figure. The test material 71 isimmersed in the tank, and an optical system like that of Fig. l (notshown) makes it possible to see when a sound beam is transmitted throughthe test material. In this case, as before, the frequency is varied fromfn to fum, e ah. zn resonant, freggencybeingadetermined by opticaltransmission beyond the specimen. The thickness calculation isdetermined as in the arrangement of Fig. 23.

In the cases of Figs. 23 and 24, it is possible to measure the thicknesst of a piece of material, the back side of which may not be accessible,for example, the wall of a closed tank, in Fig. 23, or of say acontinuously moving sheet of material, as in Fig. 24, passing throughpacking 72 in the bottom of the tank. In either case, it is alsofeasible to measure instead the velocity in test specimens of knownthickness, as, for example, in controlling the composition or processingof plastics.

In Figs. 25 and 26 is shown the application of the wedge radiator to amethod of measuring velocity, which is described in my copendingapplication, Serial No. 153,258, filed March 3l, 1950, now United StatesPatent No. 2,723,556, issued November l5, 1955, and assigned to theassignee of the present application. The particular use of the methodillustrated in Figs. 25 and 26 is for cases where the attenuation in thetest material is large or where the resonance effects of the method ofFig. 24 are too indeterminate due to perfect impedance match, as isusually the case with plastics and polymers. In the present case, Figs.25 and 26, the frequency is varied as before; and at specificfrequencies, fn, fn+1 fvwm, the two sound beams A and B beyond the testblock will be exactly out of phase and pass no light to the screen. Whenthis occurs, according to the theory of my above-noted Patent No.2,723,556.

where v1 is the known velocity in the liquid, f is the frequency, and dis the interference region spacing within the block, which, in thepresent case, cannot be observed due to opacity. However, there will be(n4-a) such 13 bands in the distance t=thickness of the block at thefrequency fn and n-l--l-m bands at fnl-m. That is,

If there is no phase change at the block to liquid interfaces for thecondition cited, exact interference beyond the block and minimum lighttransmission, then 6:1/2. If there is phase change, or if one chose someother specific optical effect (say maximum light transmission), then -l1, but its value is really of no concern. It is only necessary that thedesired optical effect at fn be repeated m times upon reaching thefrequency faim. Solving the above identity for n-lgives (wrap-12K (se)which, when substituted into Equation 35, gives Fig. 27 shows a broadfrequency band light modulator employing two identical wedge radiators81 and 82, preferably of the taper-function type IlD, previouslydescribed. Both wedges are driven from the same signal source 83 at thesame frequency f. The optical system is identical with that shown inFig. 1 and with such variations as are described for Fig. l, except thatthe lens 19 of Fig. 1 may be omitted or may be positioned so as togather the light passing aperture 17 and focus it at any desired pointor plane, say onto a photocell. It is clear that here the light passingthrough both sound beams will be acted upon as though the sound beamshad coexisted, as described in my above-noted Patent No. 2,723,556.Twice during each cycle, the two sound beams will be everywhere inphase, and the whole field will transmit light; whereas, at intermediatetimes, twice during each cycle, the two beams will be everywhere out ofphase and transmit zero light (assuming equal amplitudes of soundbeams). Thus, the light passing through the system past aperture 17 ofFig. 1 will be modulated at the frequency 2f. This same condition wouldoccur if the radiators were at and excited at, or very close to. theresonant frequency of the radiators., The advantage of the wedgeradiators is that the signal frequency may be varied over the range ofresonance of the wedges, as previously explained, thus giving abroad-band light modulator.

What is claimed is:

1. A piezoelectric vibrator having a variation of resonant frequencyfrom point to point over an extended area of its surface, electricalexciting means coupled to and common to an extended portion of saidvibrator including regions of unequal resonant frequency, and individualreceiving channel means coupled respectively to a plurality of saidportions of vibrator of unequal resonant frequency.

2. An arrangement according to claim l, in which the 5 individualreceiving channel means comprise piezoelectric pick-up elements mountedin the paths of respective vibrational waves radiated from differentportions of surface of the piezoelectric vibrator.

3. An arrangement according to claim 2, in which the piezoelectricvibrator and the piezoelectric pick-up elements are coupled by a mediumaffording an approximate impedance match with said piezoelectricvibrator and pick-up elements.

4. A multiplex communication system comprising a wedge of piezoelectricmaterial, a pair of electrical contact means between which the wedge ismounted, each said means extending over substantially the whole adjacentvibratile surface of said wedge, a plurality of piezoelectric pick-upelements mounted opposite respective portions of said wedge of differentthickness, said wedge and said pick-'up elements being coupled by amedium of suitable transmission characteristics for vibrations of saidpiezoelectric devices, a plurality of signal sources of differentfrequencies electrically coupled to said electrical contact means onsaid wedge, and a plurality of frequency selective receiving channelselectrically coupled respectively to said pick-up elements.

5. In a system for selectively exciting resonances in a multiplyresonant elastic system, a piezoelectric radiator having a variation ofresonant frequency from point to point over an extended area of itssurface, electrical exciting means of variable frequency coupled to andcornnton to an extended portion of said radiator including a pluralityof regions of unequal resonant frequency to cause the radiation into anadjacent elastic medium of waves of frequency related to the frequencyof the exciting means within the range of frequencies of saidpiezoelectric radiator, means to position the said multiply resonantelastic system in said medium in coupled relationship to said radiator,and means to detect the transmission of energy through said multiplyresonant elastic system at any of the resonant frequencies thereofwithin the range of frequencies radiated by said radiator.

6. In combination, rst and second multiply resonant elastic transmissionsystems of which systems at least the first in a piezoelectric deviceincluding discrete portions exhibiting different resonant frequencies.electrical exciting means of variable frequency coupled to saidpiezoelectric device to cause radiation into an adjacent elastic mediumtherefrom of waves of frequency determined by the frequency of theexciting means within the range of resonant frequencies of saidpiezoelectric device. said second multiply resonant system beingpositioned in the path of said radiation. and means coupled to saidsecond multiply resonant system to detect the transmission of energythrough said second multiply resonant system.

7. The combination according to claim -5 in which G0 the piezoelectricradiator is in the form of a wedge.

8. The combination according to claim 5 together with means to measurethe frequency of resonance in the specimen. MM /QTX-a'diator having avariation of resonant frequency from point to point over an extendedarea of its surface, comprising a piezoelectric quartz plate in the formof a circular cylindrical shell of uniform thickness. the generatrix ofthe cylindrical surface of which is parallel to a YZ-plane of the mothercrystal and is perpendicular to a plane through an X-axis of the mothercrystal which latter plane is inclined to -the Z-axis by an angle ofsubstantially 35 degrees in the direction of parallelism with a minorcap face.

(References on following page) 1416550 Frank May 16 1922 4962295 Langer--.uffi-: Fei). 7: 195o 1,548,260 ESPEUSChled Allg 4, 1925 5 2,505,515Arenberg Apt 25, 1950 2,084,201 KEIOIUS June 15, 1937 2,540,505 BlissFeb 6, 1951 21185-693 Mem 1an- 2 1940 2,541,067 Jaynes Feb. 13, 19512,224,700 Wolfskxll Dec. 10, 1940 2,308,360 Fair Ian. 12, 1943 2,418,964Arenberg Apr. 15, 1947 10 FOREIGN PATENTS 2,423,459 Mason July s, 19479541574 France 11111913, 1949 2,431,234 Rassweiler et al. Nov. 18, 19472,446,835 Keary Aug. 10, 1948 OTHER REFERENCES 2,447,061 Franklin Aug.17, 1948 Publication, Journal of Applied Physics, article by 2,455,389Soller Dec. 7, 1948 15 Barnes et al., March 1949, pages 286294.

